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Trigonometric Identities and Equations

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Question 1

The diagram shows parts of the curves y=8cos⁡2θy = 8\cos^2\thetay=8cos2θ and y=7−2tan⁡θcos⁡θy = 7 - 2\tan\theta \cos\thetay=7−2tanθcosθ, where θ \theta\,θ is in degrees.

Two smooth curves are shown on axes labelled y and θ, with O at the origin, arrowheads on both axes, and open circles on one curve.

a.

Show that the equation 7−2tan⁡θcos⁡θ=8cos⁡2θ7 - 2\tan\theta \cos\theta = 8\cos^2\theta7−2tanθcosθ=8cos2θ can be expressed in the form 8sin⁡2x−2sin⁡x−1=08\sin^2 x - 2\sin x - 1 = 08sin2x−2sinx−1=0

[2]
b.

Solve the inequality 7−2tan⁡θcos⁡θ>8cos⁡2θ7 - 2\tan\theta \cos\theta > 8\cos^2\theta7−2tanθcosθ>8cos2θ for 0∘≤θ<360∘0^\circ \leq \theta < 360^\circ0∘≤θ<360∘

[5]
Markscheme

Trigonometric Identities and Equations Questions

  1. A Level
  2. /Maths
  3. /Trigonometric Identities and Equations

322 exam-style questions on Edexcel A Level Maths Trigonometric Identities and Equations, covering 10.1 Angles in all four Quadrants, 10.2 Exact Values of Trigonometric Ratios, 10.3 Trigonometric Identities, 10.4 Solving Trigonometric Equations, 10.5 Harder Trigonometric Equations, and 10.6 Equations and Identities. Each one has a worked solution and a mark scheme showing where the marks go.

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